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PARTICLE PHYSICS
LECTURE 2
Georgia Karagiorgi
Department of Physics, Columbia University
2
COURSE POLICIES
Attendance
•Up to four excused absences
•
(two with notes from parent/guardian)
Valid excuses:
•
illness, family emergency, tests or athletic/academic competitions, mass transit breakdowns
Invalid excuses:
•
sleeping in, missing the train
Please no cell phones
•
Lecture materials:
http://home.fnal.gov/~georgiak/shpweb12/Lecture_Materials/Lecture_Materials.html
•
What is matter made of (c. 2000 CE)
3

Current model of matter: matter consists of
point particles (< 10-18m) interacting through
four forces.
Fundamental forces
Strong
Electromagnetic
Weak
Gravity

Strength
1
10-2
10-5
10-39
This picture (excluding gravity) summarizes the
Standard Model of particle physics.
How matter interacts: particle exchange
4



Elementary particles interact by exerting forces on each other.
The mechanism: quarks and leptons exert forces by exchanging “mediator”
particles, like photons, W or Z bosons, and gluons.
We depict particle interactions using space-time cartoons called Feynman
diagrams. Each diagram encodes quantitative physical information about the
interaction.
(decay)
time
electromagnetic interaction
(photon exchange)
strong interaction
(gluon exchange/self interaction)
weak interaction
(W±/Z exchange)
Foundations of particle theory
5



Particle physics is the study of the smallest constituents of matter. At these
size scales, matter behaves quite differently than in the macroscopic world.
Here, particles obey the rules of quantum mechanics.
Moreover, to observe the smallest size scales, we must accelerate particles
to very high energies (near the speed of light, c). At these speeds,
Newtonian mechanics is superseded by special relativity.
So, elementary particle physics describes objects that are both
very small and very fast.
To handle the physics, scientists developed a theory that incorporates
relativistic(see Session 3) and quantum(see Session 4) principles:
Quantum Field Theory.
What is matter made of (c. 2000 CE)
6
The story is far from being complete!
• “Normal” matter, described by the Standard Model, makes up only 4% of the total
matter/energy in the Universe!
• We know almost nothing about
the other 96%... more on
this later in the course.
How we determine the force laws
7



Because elementary particles are microscopic –or more correctly, at most
femtoscopic –we must usually resort to indirect observations to see the
fundamental forces at work.
Just about all particle physics measurements come from
the following sources:

Scattering: fire particles at each other and measure
the deflection (e.g. Rutherford experiment(see Session 2)).

Decays: a particle spontaneously disintegrates, and we
observe the debris (e.g. neutron decay, muon decay).

Bound states: two or more particles (oppositely charged)
form composite objects, whose properties we observe
(e.g. atom, nucleus).
From this indirect evidence, we piece together the dynamics – meaning the
force laws – obeyed by elementary particles.
Scattering example
8



In a scattering experiment, we fire particles at each other and see
what happens.
Sometimes the particles collide and form new particles
according to E = mc2 (e.g. LHC, Tevatron);
other times they just deflect (e.g. Rutherford experiment).
The amount of deflection can be predicted from a force law. Hence,
we can test whether or not we know the force law’s correct form:
How do we detect particles?
More on this in Session 5
9


When charged particles pass through matter, they ionize atoms in their path, liberating
charges, and causing the emission of detectable light (scintillators) or the formation of tracks
of droplets (cloud/bubble chambers). This is how we “see” them.
Experimental physicists use many kinds of particle detectors, including:

Geiger counters

Cloud chambers*

Bubble chambers*

Spark chambers*

Photographic emulsions*

Wire chambers

Cerenkov counters

Scintillators

Photomultipliers

Calorimeters

NOTE: most of these instruments are sensitive to electrically charged particles only!

Neutral particles cannot be directly detected easily.
* Less common these days...
Atomic excitation
10


An atom is excited when it has the potential to spontaneously produce energy. This
happens when one or more of the electrons occupy a higher-energy state; when the
electron returns to a lower energy state, the energy difference is given off in
the form of radiation.
The lowest energy state
is the ground state.
Ionization
11


Ion: positively or negatively charged particle (or part of atom)
Ions can be produced when enough energy is given to remove one or
more electrons from an atom:
E
n=2
n=2
n=1
n=1
e
p
Hydrogen atom (p+e bound state)
ionization
p
Ion (free proton)
e
Ion
(free electron)
Ionization
12

Ionization energy is the energy necessary to strip an atom of all its
electrons.
some number of
Measuring particle properties
13
A basic particle accelerator:
 Consider the parallel-plate
capacitor…
Two metal plates are given equal
but opposite charges +Q and –Q,
creating a potential difference V,
or drop in voltage, between them.
The charges set up a uniform
electric field E between the plates.
 A test charge in this region gets
accelerated.

This is the principle behind every
particle accelerator; pass charges
through an electric field to increase
their kinetic energy.
The magnetic field B
14

According to the Lorentz Force Law, the magnetic force on a charge q is:
uniform magnetic field lines (into page)



NOTE: the magnetic force is
perpendicular to both the
direction of the field and the
velocity of the (positive) test charge
(right-hand rule). If v and B are
perpendicular to each other, the charge’s trajectory will bend into a circle.
NOTE: if the charge is stationary (v=0), the magnetic force on it is zero.
Magnetic fields only affect moving charges (currents).
NOTE: the direction of the particle’s path depends on the sign
of its charge!
Measuring particle properties
15


Electric charges moving in uniform magnetic fields travel in circular
paths. The path’s radius of curvature yields important information:
By measuring the radius of curvature of a charge’s path,
physicists can determine both the momentum and the sign of the
charge. This is the primary means of particle identification
in experiments!
SYNOPSIS
16









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Session 1: Introduction
Session 2: History of Particle Physics
Session 3: Special Topics I: Special Relativity
Session 4: Special Topics II: Quantum Mechanics
Session 5: Experimental Methods in Particle Physics
Session 6: Standard Model: Overview
Session 7: Standard Model: Limitations and challenges
Session 8: Neutrinos: How experiments drive theoretical
developments
Session 9: Close up: A modern neutrino experiment
Session 10: Hands on: Design your own experiment!
Session 11: Beyond-Standard-Model Physics
Session 12: Beyond-Standard-Model Physics
History of Particle Physics
17
Late 1800’s – Early 2000’s:
Discoveries of standard model particles,
particle properties,
realization of fundamental symmetries,
experimental triumphs,
but also a lot of puzzles, frustration, confusion...
From Classical Physics…
…to Modern Physics…
…and Particle Physics today
(Standard Model)
Late 1800’s
18



Knew of atoms (άτομος = nondivisible), thought to be fundamental constituents of
matter.
Chemists and physicists were classifying the known (and yet-to-be discovered)
elements according to their chemical properties.
But trends in the periodic
table suggest some
underlying atomic
structure: i.e., atoms are
composites of smaller,
more “fundamental”
particles that determine
chemical behavior.
Mendeleev’s Periodic Table summarizes patterns in the
electro-chemical properties of the elements. In the
1800’s, scientists used these patterns to search for
“missing” elements.
Physics during the 1890’s
19
New, unstable elements (radioactivity) were being investigated by M. Curie, P. Curie, H.
Becquerel, E. Rutherford, et al.


Radioactivity: describes the emission of particles from
atomic nuclei as a result of nuclear instability. The
fact that atoms seemed to spontaneously split apart
also suggests they are not fundamental particles.
At the time, it was known that unstable elements
tended to emit three types of particles, which
were differentiated by their electric charge:
1) Alpha particles (a):
2) Beta particles (b):
3) Gamma particles (g):
+2 electric charge; about 4x proton mass
-1 electric charge; about 1/1800 proton mass
electrically neutral
Pierre and Marie Curie

Physics during the 1890’s
20
Products of elemental decays studied at the time:
The a-particle, as it turns out, is just He+2,
the nucleus of a helium atom.
It is emitted in decays like:
218
84
Po214
82 Pb  a
The b-particle is an electron (not known until 1897).
A b-decay example:
234
234
The g-particles are photons, emitted in such decays as:
Ba * 137Ba  g

137
Images: HyperPhysics

Th 91 Pa  b
90
21
The Classical Era (1897-1932)
Discovery of the electron (1897)
22

For a number of years, scientists had
generated “cathode rays” by heating
filaments inside gas-filled tubes and
applying an electric field.


Recall: we know cathode rays have electric
charge, because they can be deflected by
magnetic fields.
Question: are cathode rays some kind of charged
fluid, or are they made of charged particles (like
ions)?
J. J. Thompson
Image: NobelPrize.org

In 1897, J.J. Thomson attempted a
measurement of the charge/mass ratio of
cathode rays to see if they were particles.
Discovery of the electron (1897)
23


Image: softwarephysics.blogspot.com

Put a cathode ray into a known electric or magnetic field.
Measure the cathode ray’s deflection.
If cathode rays are composed of discrete charges, their
deflection should be consistent with the Lorentz Force Law:
Thompson’s cathode ray tube
Discovery of the electron (1897)
24




Thomson found that cathode ray deflections were indeed consistent
with the Lorentz Force, and could be particles (“corpuscles”) after
all.
The charge to mass ratio e/m was significantly larger than for any
known ion (over 1000x e/m of hydrogen). This could mean two
things:
(1) The charge e was very big.
(2) The mass m was very small.
Independent measurements of e (oil drop experiment) suggested
that, in fact, cathode rays were composed of extremely light,
negatively charged particles.
Thomson called his corpuscle’s charge the electron (from the Greek
ήλεκτρον = “amber”); eventually, this term was applied to the
particles themselves, whose mass is:
me= 0.511MeV/c2
Discovery of the electron (1897)
25



Thomson correctly believed that
electrons were fundamental
components of atoms (e.g.,
responsible for chemical
behavior).
Because atoms are electrically
neutral, he surmised that the
negatively charged point-like
electrons must be embedded in
a “gel” of positive charge such
that the entire atom is neutral.
Thomson: electrons are
contained in an atom like
“plums in a pudding”.
positively charged
“paste”
localized
electron
(negative
charge)
Thomson’s plum-pudding model of the atom.
Image: greenanswers.com
The Rutherford Experiment
26

Test of Thompson’s theory of atomic
structure (1909-1913):
E. Rutherford
Image: NobelPrize.org
Thompson’s model of atom
Rutherford’s model of atom
Image: Wikipedia.org
Recall: scattering two particles and measuring
the deflection gives information about particle
structure and interaction.
The Rutherford Experiment
27

Gold foil experiment:
Image: highered.mcgraw-hill.com
Most a-particles were not
scattered at all, but a few were
scattered through angles of 90° or
more!
The Rutherford Experiment
28

Gold foil experiment:
Image: highered.mcgraw-hill.com
Most a-particles were not
scattered at all, but a few were
scattered through angles of 90° or
more!
Rutherford: large-angle scattering
is exactly consistent with Coulomb
repulsion of two small, dense
objects.
Conclusion: scattered particle
beam is evidence of a dense,
compact, positively-charged
structure (located at the center of
the atom).
Discovery of the nucleus (1911)
29


Rutherford’s efforts formed one of the truly
great experiments of modern physics.
He quickly understood that he discovered a
new nuclear model of the atom, saying of the
result:
E. Rutherford
Image: NobelPrize.org
“It was quite the most incredible event that ever happened to me in my
life. It was almost as incredible as if you had fired a 15-inch shell at
a piece of tissue paper and it came back and hit you.”

In a later experiment (1919), he identified the nucleus of the
hydrogen atom as an elementary particle present in all other
nuclei; he called it the proton (Greek πρώτος = “first”).
The Bohr atom (1914)
30


New atomic model:
localized positive charge and electron “cloud”
Also results from spectroscopy:
Image: s-educat.blogspot.com
The Bohr atom (1914)
31


New atomic model:
localized positive charge and electron “cloud”
Also results from spectroscopy:
Recall: When you excite a
gas, it emits radiation in
certain discrete wavelengths
(spectral lines) according to
Balmer’s formula:
The Bohr atom (1914)
32


In 1914, N. Bohr developed a simple atomic model that perfectly
explained the phenomenon of spectral lines.
The three main ideas behind Bohr’s semi-classical ansatz:
1) The electron moves in uniform circular motion, with the centripetal
force provided by its Coulomb attraction to the nucleus:
2) The angular momentum of the electron in its orbit is quantized,
satisfying the constraint:
3) Therefore, the electron can have only a discrete spectrum of allowed
energies:
The Bohr hydrogen model
33




In the context of the Bohr model,
the discrete spectra seen in
atomic spectroscopy make
perfect sense.
The electron occupies discrete
orbits in the hydrogen atom.
When hydrogen is excited in an
electric field, the electron jumps
into a higher energy orbit.
Eventually, the electron will
return to a lower energy state.
Once this happens, light must be
emitted to conserve the energy
of the whole system.
Emission spectrum of the hydrogen atom.
34


In the Bohr atomic model, atoms consisted of
just protons and electrons.
However, there was a major problem: most
elements were heavier than they should have
been.
(He charge is +2e, but weighs 4mp;
Li charge +3e, but weighs 7mp; etc.)
J. Chadwick
Image: NobelPrize.org
Discovery of the neutron (1932)
35




In the Bohr atomic model, atoms consisted of
just protons and electrons.
However, there was a major problem: most
elements were heavier than they should have
been.
(He charge is +2e, but weighs 4mp;
Li charge +3e, but weighs 7mp; etc.)
To account for the missing mass in heavier
elements, nuclei had to contain other particles
comparable in mass to the proton (1 GeV/c2)
but with no electric charge.
The mysterious massive, neutral particle inside
atomic nuclei eluded detection until 1932, when
J. Chadwick observed the neutron in an a-Be
scattering experiment.
J. Chadwick
Image: NobelPrize.org
End of an Era (1897-1932)
36





1927: New Wrinkle…
Antimatter
P. Dirac attempted to combine quantum mechanics
with the relativistic energy formula:
PROBLEM: the theory allows both positive and
negative energy solutions!
Dirac’s interpretation: the positive solutions are
ordinary particles; the negative solutions are antimatter.
But was anti-matter real, or just a mathematical
artifact?
P. Dirac
Image: NobelPrize.org
Discovery of antimatter (1932)
37




In 1932, C. Anderson observed the
anti-electron (positron), validating
Dirac’s theory.
Feynman’s explanation of negative
energies: they are the positive
energy states of anti-particles!
Anti-matter is a universal feature
of quantum field theory; all
particles have matching antiparticles.
Anti-particles have the same mass
as their particle partners, but
opposite quantum numbers (charge,
lepton number, etc.)
Notation:

Particle:
e ,p
Antiparticle: e  ,e , p
Discovery of the positron in a cloud chamber
by C. Anderson
Image: J. Griffiths, Intro to Elementary Particles
Meanwhile… (1900-1924)
38




A new particle, the field quantum
The discovery of the photon, the quantum of the
electromagnetic field, marked a major departure from
classical physics.
As with the developing picture of the atom, it took
several decades (and several incontrovertible
experiments) before physicists accepted the existence
of the photon.
But before we get into that, let’s talk about what
classical physics actually had to say about
electromagnetism.
Classical electrodynamics
39

Work by J.C. Maxwell in the mid/late 1800s:
the EM field could be understood in terms of
four equations:
J.C. Maxwell
The University of York

These are Maxwell’s equations in the vacuum, relating the electric and
magnetic field.
Classical electrodynamics
40

Maxwell’s equations predict self-propagating, transverse electric
& magnetic (electromagnetic) waves, aka light, which travel at
speed c=3x108m/s
and have frequency
f=c/l
Image: HyperPhysics.com
Classical electrodynamics
41

A beautiful theory…
The implications of the Maxwell
Equations –namely, the
appearance of electromagnetic
fields to observers in different
inertial reference frames –
inspired scientists (Poincaré,
Einstein) to develop special
relativity.

But, when trying to
explain thermal radiation
(light emitted by hot
objects), the theory
completely fails!
Failure of classical electrodynamics
42

When light is emitted by
hot objects, the intensity of
the light always varies
continuously with the
wavelength –unlike atomic
spectra –and the spectrum
has a characteristic shape.
Examples of blackbodies:
stars, light filaments,
toaster coils, the universe
itself!

This so-called blackbody
spectrum (or Planck
spectrum) always peaks at
a wavelength that depends
on the surface temperature
of the object.
Failure of classical electrodynamics
43

“Ultraviolet catastrophe”

A study of blackbody radiation with
classical E&M and statistical
mechanics (the Rayleigh-Jeans Law)
predicts that the emitted intensity
varies with frequency and
temperature as:
f


f
This means that as the light
frequency increases into the UV, the
intensity becomes infinite!
This nonsensical answer was such an
embarrassment for the theory that
physicists called it the “ultraviolet
catastrophe”.
Planck’s solution: light quanta
44



In 1900, using arguments from statistical mechanics (the theory of bodies
in thermal equilibrium), M. Planck derived a theoretical curve that fit the
blackbody spectrum perfectly:
However, to get this result, Planck had to assume that thermal radiation is
quantized; that is, it’s emitted in little “packets” of energy, photons,
proportional to the frequency n:
The quantity h, called Planck’s constant, was determined from the fit to the
blackbody spectrum. It turned out to be a fundamental constant of nature,
and has the value:
Are photons real?
45




In order to explain blackbody emission spectra, Planck
needed to assume that thermal radiation is emitted in
bundles whose energy comes in integral multiples of hn.
This suggested that light could actually be quantized
(it’s a particle). But most of the experimental evidence
(and Maxwell’s Equations) at the time said that light is
a wave.
M. Planck
NobelPrize.org
So is light a particle, or a wave? As it turns out, light
can behave like a particle if you are performing the right kind of
experiment!
At first, Planck did not really believe in the light quantum, and most
physicists did not accept its existence until faced with undeniable
evidence from two phenomena:
1) The photoelectric effect
Evidence for particle nature of light
2) Compton scattering
Photoelectric effect (1905)
46

In the 1800’s, it was discovered that shining light onto certain metals
liberated electrons from the surface.
Experiments on this photoelectric effect showed odd results:
1) Increasing the intensity of the light increased the number of electrons,
but not the maximum kinetic energy of the electrons.
2) Red light did not liberate electrons, no matter how intense it was!
3) Weak violet light liberated few electrons, but their maximum kinetic
energy was greater than that for more intense long-wavelength beams!


In 1905, A. Einstein showed that these results made perfect sense in
the context of quantization of the EM field, where photon energy
is proportional to frequency. If photons of energy E=hn strike
electrons in the surface of the metal, the freed electrons have a
kinetic energy:
The work function f is a constant that depends on the metal.
A. Einstein
NobelPrize.org
Compton scattering (1923)
47
A. H. Compton
NobelPrize.org

In 1923, A.H. Compton found that light scattered from a particle at rest is shifted in wavelength by an
amount:
Here, lc=h/mc is the Compton wavelength of the target mass m.


There is no way to derive this formula if you assume light is a wave, but if you treat the incoming light
beam like a particle with energy E=hn, Compton’s formula drops right out!
Hence, the Compton Effect proved to be the decisive evidence in favor of the quantization of the EM
field into photons.
When is field quantization important (observable)?
48



Even on the atomic scale, quantization of the EM field is a tiny effect
In a bound state (like H = proton + electron), huge numbers of photons
are streaming back and forth, effectively “smoothing out” the EM field in
the atom.
Only in elementary particle processes involving single photons (Compton
scattering, photoelectric effect) does field quantization become
important.
49
On to the particle zoo (1932-1960)
Field quantization in nuclear physics
50


Field quantization, once accepted for the
electromagnetic field, was quickly applied to other
calculations.
One was the physics of the atomic nucleus, which
gets very complicated after hydrogen.
 QUESTION:
How are protons in heavy
atoms bound inside the 1 fm “box” of
the nucleus?
 Shouldn’t the electrostatic repulsion of
the protons blow the nucleus apart?
Nuclear force model (1934)
51




Evidently, some force is holding the nucleus
together: the “strong force.”
Inside the nucleus, the strong force has to
overwhelm the EM force, but outside, on the
atomic scale, it should have almost no effect.
How to accomplish this? Assume the strong force
has a very short range, falling off rapidly to
zero for distances greater than 1 fm.
H. Yukawa: force may vary as:
where a
1 fm is the range.
H. Yukawa
Image: NobelPrize.org
Quantization of the nuclear field
52





Yukawa’s Model: the proton and neutron are attracted to each other
by some sort of field, just like the electron is attracted to the proton
by the electromagnetic field.
The nuclear field should be quantized; that is, it is mediated by an
exchanged quantum, as the electromagnetic field is mediated by the
photon. So, there should exist a new, detectable particle!
An interesting issue: because the range of the nuclear field is so
small, the exchanged quantum of the strong force must be massive
(this is due to the Uncertainty Principle –next slide and later…).
Yukawa calculated the mass of the strong mediator, and found it to
be about 300me, or mp/6.
Because its mass fell between that of the proton and electron, he
called it a meson (Greek = “middle-weight”), distinguished from the
electron (lepton = “light-weight”) and the neutron and proton
(baryon = “heavy-weight”).
Estimate of Yukawa meson mass
53

Use Heisenberg’s uncertainty principle:
to estimate the Yukawa meson mass
Estimate of Yukawa meson mass
54





When two protons in a nucleus exchange a meson (mass m), they
temporarily violate energy conservation.
The Heisenberg Uncertainty Principle says this is OK, as long as the
amount of energy borrowed ( E) is “paid back” in a time ( t) such
that:
In this case, we need to “borrow” an energy E=mc2 long enough
for the meson to make it across the nucleus from one proton to
another.
Since the meson will probably travel at some substantial fraction of
the speed of light, the time it takes to cross the nucleus is roughly:
So, the meson mass is:
Discovery of Yukawa’s meson?
55






In 1937, two groups studying cosmic ray air showers found
particles of approximately the mass predicted by Yukawa.
Did this confirm Yukawa’s theory of strong interactions?
Not exactly… it turned out that the particles observed by
cosmic ray physicists had the wrong lifetimes (much too long:
~ 2 ms) and masses (a little too light: ~ 100 MeV/c2).
By 1947, physicists realized that the cosmic ray particles
were not the expected nuclear meson, but rather a
completely unexpected elementary particle: the m (“muon”).
Theorists were not happy. Rabi: “Who ordered that?”
About the same time, other short-lived particles known as
pions (p) were also discovered.
Particle spectrum extends…
56





Proton, electron, neutron
Photon
Muon
Pions
+ antiparticles
+Neutrinos…
57

Postulated to save conservation of energy!





In the study of radioactive decays (esp. b-decay),
physicists found that many reactions appeared to
violate energy conservation.
Conclusion 1 (Bohr): nuclear decays do actually
violate energy conservation.
Conclusion 2 (W. Pauli): the missing energy is
carried off by another neutral particle which
hadn’t been detected (as of 1930).
In 1932, E. Fermi incorporated Pauli’s idea into his
theory of nuclear decays. He called the missing
particles neutrinos (“little neutral ones”).
Major assumption: neutrinos almost never interact
with ordinary matter, except in decays.
W. Pauli
E. Fermi
NobelPrize.org
Discovery of neutrinos (1950s)
58




By introducing neutrinos (symbol n) to radioactive decay,
conservation of energy was restored. Decay reactions
started to look like this:
By 1950, there was compelling theoretical evidence for
neutrinos, but no neutrino had ever been experimentally
isolated.
Finally, in the mid-1950s, C. Cowan and F. Reines came up
with a method to directly detect neutrinos using “inverse”
b-decay:
A difficult experiment: Cowan and Reines set up a large
water tank outside a commercial nuclear reactor, expecting
to see evidence of the above reaction only 2 to 3 times per
hour (which they did). Conclusion: (anti) neutrinos (n’s) exist.
C. Cowan and F. Reines
Image: CUA
Antineutrinos?
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Because all particles have anti-particles, physicists assumed that
neutrinos must have corresponding anti-neutrinos.
But does anything distinguish a neutrino from an anti-neutrino?
From the results of Cowan and Reines, the reaction below must
occur:
If anti-neutrinos are the same as neutrinos, the anti-neutrino
version of this reaction must also occur:
In fact, in the late1950s, R. Davis and D.S. Harmer found that the
anti-neutrino reaction does not occur. Therefore, something is
different about the anti-neutrino that forbids the process. But
what?
A new conservation law
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A rule of thumb (R. Feynman): a reaction will be observed
unless it is expressly forbidden by a conservation law.
So what conservation law does the anti-neutrino reaction
violate? Conservation of energy and electric charge are
obeyed, so it must be something else.
In 1953, E.J. Konopinski and H.M. Mahmoud proposed the
existence of a new quantum number that explained why
certain reactions worked while others did not.
They assigned a lepton number L=+1to the electron,
muon, and neutrino, and L=-1to the positron, antimuon,
and antineutrino. All other particles got L=0. In any
reaction, this lepton number had to be conserved!
Lepton number conservation
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To apply conservation of lepton number, just add up the lepton numbers on each
side of the reaction and see if they agree.
The neutrino reaction occurs because:

The antineutrino reaction doesn’t occur because:
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In view of lepton number conservation, the charged pion and muon decays should
actually be written:
Lepton FLAVOR number conservation
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Experimentally, the following reaction (though it obeys energy,
charge, and lepton number conservation) never occurs:
Why? Apparently, the absence of this reaction suggests a law of
conservation of “mu-ness,” but that alone wouldn’t explain why
muons can decay like this:
Conclusion: something about the n’s in the second reaction makes it
occur.
The Answer: there are two kinds of neutrinos: one associated with
the electron (ne) and one with the muon (nm).
Therefore, we now have an electron number Le and a muon
number Lm to account for all forbidden and allowed processes.
Lepton conservation becomes electron number and muon number
conservation.
Decays and lepton flavor conservation
63
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In the context of Le and Lm conservation, we can now
account for all forbidden and allowed decays…
Note how all of the decays conserve charge and
energy as well as lepton flavor.
Particle spectrum extends…
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Proton, electron, neutron
Photon
Muon
Pions
+ antiparticles
+ neutrinos
+ strange particles
Discovery of strange particles (1947)
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By 1947, the catalog of elementary particles
consisted of the p, n, p, m, e, and the n (and the
anti-particles). The overall scheme seemed pretty
simple.
However, at the end of that year, a new neutral
particle was discovered: the K0 (“kaon”):
In 1949, a charged kaon was found:
The K’s behaved somewhat like heavy p’s, so they
were classified as mesons (“mass roughly between
the proton and electron mass”).
Over the next two decades, many more mesons
were discovered: the h, the f, the w, the r’s, etc.
Bubble chamber photo of kaon decay (U of Birmingham)
65
More strange particles (1950)
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In 1950, C. Anderson observed another particle that looked like the K, but
decayed via the reaction:
The L is heavier than the proton, making it a baryon like the p and n.
Over the next decade, as particle accelerators started to increase in energy,
many more (increasingly heavy) baryons were discovered: the S’s, the X’s, the
’s, etc.
Struggling to fit new particles into existing theories, physicists viewed the
growing groups of mesons and baryons with increasing dismay:
When Nobel prizes were first awarded in 1901, physicists knew something of just
two objects which are now called “elementary particles”: the electron and the
proton…. I have heard it said that “the finder of a new elementary particle used
to be rewarded by a Nobel Prize, but such a discovery now ought to be punished
by a $10,000 fine.”
-W. Lamb, Nobel Prize Acceptance Speech, 1955
A new conservation law
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QUESTION: Experiments in the 1950s showed that there were many unstable
baryons, but the proton was not one of them. Why didn’t the proton decay?
In 1938, Stückelberg proposed an explanation of the proton’s stability. The
method is familiar: he introduced a new quantum number, and assumed that it
was conserved in all interactions.
The new quantum number, often written A, is called the baryon number. The
baryons get A=+1, and the antibaryons get A=-1; all other particles get A=0.
Baryon number conservation explains why b-decay works, and p-decay does
not:
NOTE: no known reaction seems to conserve meson number, so we don’t have to
worry about conservation of mesons.
Yet another quantum number (S)
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“Strange” Behavior: The new mesons and baryons discovered during
the 1950s all had the following properties:
1) They are produced on short timescales (10-23s)
2) But they decay relatively slowly (10-10s)
This suggests the force causing their production (strong force) differs
from the force causing their decay (weak force).
In 1953, M. Gell-Mann and K. Nishijima introduced a new quantum
number, strangeness (S), to explain this behavior.
According to this scheme, strangeness is conserved in strong interactions,
but not conserved (violated) in weak decays.
IMPORTANT POINT: In addition, particles with non-zero S are always
produced in pairs –no interaction produces just one strange particle.
Conservation of strangeness
69
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A p-p collision may produce the following products; here S is
conserved:

The K’s have S=+1, the S’s and L have S=-1, and the p, p, and
n have S=0.
When these particles decay, S is not conserved:

Strong processes conserve S; weak processes do not!

Summary of particle zoo (1960)
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Leptons: e, m, ne, nm. Lightest particles. Lepton
flavor number is conserved in all interactions.
Mesons: p,h,f,w,r, … Middle-weight particles.
There is no conserved “meson number”.
Baryons: p, n, S,X,L, … Heaviest particles.
Baryon number A is always conserved. Strangeness
S is conserved sometimes (strong interactions) but not
always (weak decays).
The point: things seemed like a real mess! No one
knew how to predict particle properties. New
conservation laws were invented to explain
reactions.
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Quark Era (1960-1978)
The Eightfold Way
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Finally, in 1961, Gell-Mann brought some order to the chaos by
developing a systematic ordering of the elementary particles.
He noticed that if he plotted the mesons and baryons on a grid
of strangeness S vs. charge Q, geometrical patterns emerged.
The lightest mesons and baryons fit into hexagonal arrays:
M. Gell-Mann
Baryon Octet
Images: physics.fsu.edu
Meson Nonet
Image: NobelPrize.org
The Eightfold Way
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Gell-Mann called his organizational scheme the “Eightfold Way”.
Note that other figures were allowed in this system, like a
triangular array incorporating 10 of the heavier baryons.
M. Gell-Mann
Image: NobelPrize.org
Baryon Decuplet
Images: physics.fsu.edu
Prediction of new baryons (1964)
74
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Like the Periodic Table of the elements, the Eightfold Way yields simple relations
between the hadrons.
Gell-Mann/Okubo mass formula: relates masses of the members of the baryon
octet:
Similarly, a mass formula for the baryon decuplet:
KEY POINT: In 1963, the W was not yet observed. Gell-Mann used the
Eightfold Way to predict its mass, charge, and strangeness.
In 1964, the W was found, and had exactly the properties predicted!
The quark model (1964)
75
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The patterns of the Eightfold Way evoke the periodicities of the Table of the
Elements.
In 1964, Gell-Mann and G. Zweig proposed an explanation for the structure in the
hadron multiplets: all hadrons are composed of even more fundamental constituents,
called quarks.
According to their quark scheme, quarks came in three types, or “flavors”:
up (u), down (d), and strange (s).
To get the right hadronic properties, Gell-Mann gave his quarks fractional electric
charge:
The quark model (1964)
76
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The quark model has the following conditions:
1) Baryons are composed of three quarks;
antibaryons are composed of three antiquarks.
2) Mesons are composed of quark-antiquark pairs.
Using these rules, the hadronic
multiplets are easily constructed…
Baryon decuplet
The quark model (1964)
77
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NOTE: quarks have never actually been observed!
There is no such thing as a free quark (more on this
later…). However, scattering experiments suggest
hadrons do have a substructure (analogous to
Rutherford scattering of atoms).
The quark model (1964)
78
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Until the mid-1970s, most physicists did not accept
quarks as real particles.
Then, in 1974, two experimental groups discovered a
neutral, extremely heavy meson called the J/y.
The J/y had a lifetime about 1000 times longer than
other hadrons in its mass range.
A simple way to explain its properties uses the quark
model. A new quark, called charm (c), was introduced;
and the J/y was shown to be a bound state of a
charm-anticharm pair (sometimes called “charmonium”).
We have since discovered the bottom (beauty) quark, in
1977, and the top (truth) quark, in 1995.
The quark model: btw…
79
http://www.symmetrymagazine.org/breaking/2012/01/11/belle-experiment-makes-exotic-discovery/
80
Standard Model (1978-present)
The Standard Model Now
81